Using Kirchhoff's laws for multiple batteries and resistors

[Bolter]

Homework Statement

See full question below

Relevant Equations

Kirchhoff 1st and 2nd law

Hey everyone!

Had an attempt at this circuit question, but wanted to check if I got the set up right in order to find the current in the 3rd wire?

Here is what I have done

Thanks!

 

[jbriggs444]

You have done well, showing the internal resistance in each battery as an explicit external resistor in series.

However, there is a problem with the depiction of the "mid-point" connections. The three ohm wire connects at the midpoints of the two ohm and the four ohm wires. It would be best to split the two ohm "resistor" at its midpoint and to do the same for the four ohm "resistor".

Because the drawing is misleading, the equations you constructed from it are not correct.

 

[Bolter]

You have done well, showing the internal resistance in each battery as an explicit external resistor in series.

However, there is a problem with the depiction of the "mid-point" connections. The three ohm wire connects at the midpoints of the two ohm and the four ohm wires. It would be best to split the two ohm "resistor" at its midpoint and to do the same for the four ohm "resistor".

Because the drawing is misleading, the equations you constructed from it are not correct.

So would this be a much preferred circuit diagram then?

I think my loop equations will be the same as before if I use Kirchhoff's law on left & right loop

 

[jbriggs444]

Very nice drawing. And now that I look again your equations were correct to start with.